1. Coordination Chemistry II: Bonding
Chapter 10

2. Thermodynamic Data
Stability constants or formation constants are often used to indicate bond strengths.
What does a high formation constant mean?
Thermodynamic data is most valuable in predicting relationships among similar complexes.
Formation constants can be affected by enthalpy and entropy changes.
Table 10-2 and the chelate effect.

3. Magnetic Susceptibility
Diamagnetic versus paramagnetic complexes.
Measurement (Figure 10-1).
Commonly provides mass susceptibility per gram.

4. Contributions to the Magnetic Moment
Spin magnetic moment
S = maximum total spin in the complex
O atom
Orbital angular momentum
Characterized by the quantum number L which is equal the maximum possible sum of ml values.

5. Contributions to the Magnetic Moment
Usually, the spin-only moment is sufficient to calculate the magnetic moment.
Especially for the first transition series
where g is approximated to be 2 and n is the number of unpaired electrons.
Determine the spin-only and complete magnetic moment for Fe.

6. Electronic Spectra
Orbital energy levels can be obtained directly from electron spectra (covered earlier).
This chapter illustrates simple energy level diagrams that are commonly more complex.
Based upon subtle differences in electronic spectra, the structure may be predicted with some success.

7. Theories of Electronic Structure
Valence Bond Theory – Not commonly used, but the hybrid notation is still common.
Crystal Field Theory – An electrostatic approach used to describe the splitting in metal d-orbital energies. Does not describe bonding.
Ligand Field Theory – A more complete description of bonding in terms of the electronic energy levels of the frontier orbitals. Commonly does not include energy of the bonding orbitals.
Angular Overlap Method – Used to estimate the relative magnitude of the orbital energies in a MO calculation.

8. Valence bond Theory (hybridization)
A set of hybrid orbitals is produced to explain the bonding.
Octahedral – d2sp3 (6 hybrid orbitals of equal energy)
Tetrahedral - ??
Uses ‘inner’ and ‘outer’ orbitals to explain the experimentally determined unpaired electrons.
The magnetic behavior determines which d orbitals (e.g. 3d or 4d) are used for bonding (Figure 10-2).

9. Valence Bond Description
Two configurations are possible for d4-d7 ions.
Fe(III) has 5 electrons in the d-orbitals.
One unpaired electron, the ligands are ‘strong’ and force the metal d electrons to pair up.
Strong-field (bind strongly)  low spin complex
The hybridization orginates from the 3d inner orbitals (d2sp3).
Five unpaired electrons, the ligands are ‘weak’ and cannot force the metal d electrons to pair up.
Weak-field (bind weakly) high spin
The hybridization originates from the 4d outer orbitals (sp3d2).

10. Crystal Field Theory
The ligand octahedral field repels electrons in the d orbitals.
Amount of repulsion depends on the orientation of the d orbitals.
are oriented directly toward these ligands.
dxy, dxz, and dyz are directed between the ligands.
Which set is lower in energy?

11. Crystal Field Theory
The average energy of the d-orbitals in the present of the octahedral field is greater than than of the free ion.
Energy difference between the two sets is equal to O.
The t2g set is lowered by 0.4 O and the eg set is raised by 0.6 O.
Crystal field stabilization energy (CFSE) – The energy difference between the actual distribution of electrons and that for all electrons in the uniform field.
Equal to LFSE (later)
Drawbacks

12. Ligand Field Theory – Octahedral Complexes
Consider -type bonding between the ligands and the metal atom/ion.
Construct LGOs (performed previously).
What is the reducible representation?
Construct the LGOs (pictures).
Construct the molecular orbitals with the metal orbitals.
Same symmetry types.
A group of metal orbitals do not have the appropriate symmetry?
Which orbitals are these? Symmetry type? Bonding?
Look at Figure 10-5.

14. SF6
py orbitals on fluorine

16. Ligand Field Theory – Octahedral Complexes
The six bonding orbitals are largely filled by the electrons from the ligands.
The higher MOs (e.g. t2g and eg) are largely filled by the electrons on the metal atom/ion.
The ligand field treatment largely focuses on the t2g and higher orbitals.
The split between the two sets of orbitals, t2g and eg, is called O.

17. Ligand Field Theory – Octahedral Complexes
Ligands whose orbitals interact strongly with the metal orbitals are called strong-field ligands.
Strong-field  large O  low spin (why?)
Ligands with small interactions are called weak-field ligands.
Weak-field  small O  high spin (why?)
For d0 – d3 and d8-d10 only one electron configuration is possible (no difference in net spin).
For d4 – d7 there is a difference between strong- and weak-field cases.

19. Low Spin Versus High Spin
Energy of pairing electrons
c is the Coulombic energy of repulsion (always positive when pairing) and e is the quantum mechanical exchange energy (always negative).
e relates to the number of exchangeable pairs in a particular electron configuration. This term is negative and depends on the number of possible states.
Determine c and e for a d5 metal complex (low and high spin).

20. Low Spin Versus High Spin
The relationship between O, c, and e determines the orbital configuration.
 is largely independent on the ligands while O is strongly dependent.
Look at Table 10-6 which gives these parameters for aqueous (aqua) ions.
O for 3+ ions is larger than O for 2+ ions.
O values for d5 are smaller than d4 and d6.

22. Low Spin Versus High Spin
If O>, there is a lower energy upon pairing in the lower levels (low spin).
If O<, there is a lower energy with unpaired electrons in the lower levels (high spin).
In Table 10-6, [Co(H2O)6]3+ is probably the only complex that could be low spin.

23. Ligand Field Stabilization Energies (LFSE)
The difference (1) the total energy of a coordination complex with the electron configuration resulting from ligand field splitting of the orbitals and (2) the total energy for the same complex with all the orbitals equally populated is the LFSE.
-2/5O + 3/5O (d4 to d7 complexes)
Table 10-7

25. Enthalpy Relationships
M2+(g) + 6H2O(l)  [M(H2O)6]2+
H2O is a weak field ligand.
What accounts for the general decrease in H?
What about the double hump?
O is determined generally determined experimentally.

26. Pi Bonding in Octahedral Complexes
The x and z axes must be taken as a single set producing a combined LGO set. Why?
Be able to derive the reducible representation.
 = T1g + T2g + T1u + T2u
How will the LGOs combine with orbitals from the metal atom/ion?
Discuss the overlap between the -bonding LGOs and the p-orbitals of T1u symmetry.

27. Pi Bonding in Octahedral Complexes
The main addition to the interaction diagram is between the t2g orbitals of the metal and LGOs.
These were nonbonding when only considering -type bonding (look at Figure 10-5).
Pi bonding may occur when the ligands have available p or * molecular orbitals.

28. Ligands with Empty * Orbitals
Examine the example for the CN- ligand in the book (Figure 10-9).
The HOMO forms the LGOs from -type bonding (already discussed previously).
The LUMO, 1*, also forms a reducible set of LGOs (T1g + T2g + T1u + T2u).
Examine Figure to illustrate effectiveness of overlap.

30. Ligands with Empty * Orbitals
The resulting t2g LGOs are generally higher in energy than the initial t2g orbitals on he metal.
Bonding/antibonding t2g orbitals will result.
What will this do to O and the bond strength?
Figure
This is termed as metal-to-ligand  bonding or  back-bonding.
Some of the electron density in the d orbitals on the metal is donated back to the ligands.
The ligands are termed as -acceptor ligands.

32. Ligands with Filled -Type Orbitals
Ligands such as F- or Cl- will possess molecular  orbitals that possess electrons.
This set of ‘t2g’ orbitals are generally lower in energy than the t2g orbitals on the metal.
What are the consequences?
Examine Figure
Ligand-to-metal  bonding (-donor ligands).
This bonding is generally less favorable. Why?

33. Square-Planar Complexes
The y-axis is pointed toward the center atom.
LGOs for sigma-type bonding.
The -bonding orbitals on the x- and z-axes have to be considered separately? Why?
These are termed as  (px) and  (pz)
Examine Table 10-9.
What is the symmetry of a square-planar complex?

34. Square-Planar Complexes Sigma-Type Bonding Only
Finding the LGOs.
red = A1g + B1g + Eu
What are the orbitals on the central metal atom that can interact with these LGOs?
Inspecting the character table reveals that the metal d-orbitals are split into three representations. Why?
Examine Figure
The energy difference between the eg/b2g nonbonding orbitals and the a1g antibonding is .

36. Square-Planar Complexes Including Pi-Bonding
px = A2g + B2g + Eu ()
What are the interacting orbitals on the metal?
pz = A2u + B2u + Eg ()
The effective overlap of the p orbitals on the metal to form  bonds is small. Why?
Examine Figure

38. The ‘Sets’ of Orbitals in Figure 10-15
The 1st set contains bonding orbitals (mostly sigma).
8 electrons from the ligands largely fill these orbitals.
The 2nd set contains 8 -donor orbitals of the ligands.
This interaction is small and decreases the energy differences in orbitals the next higher set.
The 3rd set is primarily metal d-orbitals with some modifications due to interactions with the ligands.
3, 2, and 1 are in this set.
The 4th set largely originates from the * orbitals of the ligands (if present).
One of the main effects of these orbitals is the increase in the gap energy labeled 1.

39. Angular Overlap (Crystal Field)
Estimates the strength of interaction between individual ligand orbitals and d-orbitals based on the overlap between them. These values are then combined for all ligands and d-orbitals.
The value for a given d-orbital is the sum of the numbers for the appropriate ligands in a column.
This number can be positive or negative depending on location of the ligand and d-orbitals.
The value for a given ligand is the sum of the numbers for all d-orbitals in the row.
This number can also be positive or negative depending on location of the ligand and d-orbitals.

40. Angular Overlap
Sigma-donor interaction (no pi-orbitals are available).
[M(NH3)6]n+
The strongest interaction is between the metal dz2 orbital and a ligand p-orbital (or appropriate MO).
Describe the interaction based on this method.
Table and Figure

41. Angular Overlap Pi-acceptor ligands (available -type orbitals).
Strongest interaction is between dxz and * on the ligand.
The * orbitals are almost always higher in energy.
Reverse the signs.
Figure and Table 10-12
There is a lowering of 4e due to this interaction.
Why is magnitude e always smaller than that of e?
Understand -donor interactions.

42. The Spectrochemical Series
 depends on the relative energies and the degree of overlap.
How ligands effect 
-donor ligands
-donating
-accepting (or back bonding)
Understand the spectrochemical series (page 368)

43. Magnitude of e, e, and 
Changing the metal and/or ligand effects the magnitudes of e and e, thereby changing the value of .
Aqua species of Co2+ and Co3+
[Fe(H2O)6]2+ versus [Fe(H2O)6]3+
Tables and (Angular Overlap)
e > e (always)
Values decrease with increasing size and decreasing electronegativity
Negative values for e. Why?

45. The Jahn Teller Effect
There cannot be unequal occupation of orbitals with identical energies. The molecule will distort so that these orbitals are no longer degenerate.
Cu(II) d9 ion, The complex will distort. How?
The low-spin Cr(II) complex is octahedral with tetragonal distortion (Oh  D4h)
Two absorption bands are observed instead of one.

47. Determining Four- and Six-Coordinate Preferences
General angular overlap calculations of the energies expected for different number of d electrons and different geometries can give us some indication of relative stabilities.
Larger number of bonds usually make the octahedral complexes more stable. Why are the energies equal in the d5, d6, and d7 cases?
Figure

49. Determining Four- and Six-Coordinate Preferences
The success of these simplistic calculations is variable.
The s- and p-orbitals of the metal are not included.
No -type interactions are included in Figure
The orbital potential energies for the metals change with increasing atomic number (more negative).
Can add –0.3e  (increase in Z) as a rough correction to the total enthalpy.

50. The Process for a Complex of D3h Symmetry
Construct the sigma-type bonding LGOs for the complex.
Determine the interacting orbitals on the center atom.
Construct a table to determine e (and e if appropriate).
Construct the MO diagram and overlap energy figure.
Homework: Determine the e contribution.